Question

find the value of X and y
a²x+b²y=c²
b²x+a²y=d²​

Answer 1

$a^2x + b^2y = c^2$ (i)

$b^2x + a^2y = d^2$ (ii)

On (i) - (ii)

$a^2x + b^2y - ( b^2x + a^2y) = c^2 - d^2$

$a^2x + b^2y - b^2x - a^2y) = c^2 - d^2$

$x(a^2 - b^2) - y(-b^2 + a^2) = c^2 - d^2$

$(x - y)(a^2 - b^2) = c^2 - d^2$

$x - y = \frac{c^2 - d^2}{a^2 - b^2}$

$x = \frac{c^2 - d^2}{a^2 - b^2} + y$

$y = \frac{c^2 - d^2}{a^2 - b^2} - x$